Systems and methods for performing quantum computations

Abstract

Apparatus and methods for performing quantum computations are disclosed. Such apparatus and methods may include identifying a first quantum state of a lattice having a system of quasi-particles disposed thereon, moving the quasi-particles within the lattice according to at least one predefined rule, identifying a second quantum state of the lattice after the quasi-particles have been moved, and determining a computational result based on the second quantum state of the lattice.

1. A quantum computing system, comprising:
 a lattice having a plurality of non-Abelian anyons disposed thereon, wherein said non-Abelian anyons are excitations of least energy states of a system of real particles that form the lattice; 
 means for identifying a first quantum state of the lattice; 
 means for moving the non-Abelian anyons within a 2D+1 space-time of the lattice; 
 means for identifying a second quantum state of the lattice after the non-Abelian anyons are moved; and 
 means for determining a computational result based on the first and second quantum states of the lattice. 
 
     
     
       2. The system of  claim 1 , wherein the plurality of non-Abelian anyons are arranged on the lattice to satisfy a predefined excitation above a least energy state of the system of real particles. 
     
     
       3. The system of  claim 2 , wherein the real particles are arranged to form a first superposition of multi-loops and arcs, said first superposition defining the first quantum state of the lattice. 
     
     
       4. The system of  claim 3 , wherein the second quantum state is defined by a second superposition of multi-loops and arcs formed on the lattice after the non-Abelian anyons are moved. 
     
     
       5. The system of  claim 1 , wherein the lattice has a number of lattice sites, and the plurality of non-Abelian anyons are distributed among only a subset of the lattice sites. 
     
     
       6. The system of  claim 5 , wherein the plurality of non-Abelian anyons are distributed dilutely and the real particles are distributed on an edge lattice in proportion to a valence of the edge lattice. 
     
     
       7. The system of  claim 6 , wherein the edge lattice is a triangular lattice and the proportion is ⅙. 
     
     
       8. The system of  claim 1 , wherein the non-Abelian anyons are set on bonds of a triangular sub-lattice formed within a Kagome lattice. 
     
     
       9. The system of  claim 1 , wherein the real particles are bosons. 
     
     
       10. The system of  claim 1 , wherein the real particles are fermions.